On Application Of Matlab To The Motion Of A Finitely Damped String On Sobolev Spaces
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AUTHOR(S)
Egbuhuzor Udechukwu P., Ugbene Ifeanyichukwu, EzeEverestus O
KEYWORDS
Keywords and phrases: motion, Sobolev space, mechanical system, vibrations, damped strings, plucking technique, nylon and steel strings. 2010 mathematical subject classification: 70E15, 70E18, 70F25
ABSTRACT
ABSTRACT: The problem of vibrations of plucked strings was investigated. The objective is to determine the vibrational behaviour of a guitar with nylon and steel strings. The derived Newton's second law of motion [7] with damping coefficient was used and the equation of the form
T(x) sinθ+T(x+∆x) sinβω∆xU_t=mU_tt . . . (1)
Was considered. The method of separable variable was applied and we obtained
U_xxKU_t= 1/C^2 U_tt . . . (2)
The result shows that nylon strings decay mainly as a result of internal damping in the strings while steel strings decay due to air viscosity. Therefore we conclude that nylon strings are under less tension than steel strings [5].
REFERENCES
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